Problem: Omar is 12 years younger than Daniel. For the last four years, Daniel and Omar have been going to the same school. Eight years ago, Daniel was 3 times as old as Omar. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Daniel and Omar. Let Daniel's current age be $d$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $d = o + 12$ Eight years ago, Daniel was $d - 8$ years old, and Omar was $o - 8$ years old. The information in the second sentence can be expressed in the following equation: $d - 8 = 3(o - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = d - 12$ . Substituting this into our second equation, we get the equation: $d - 8 = 3($ $(d - 12)$ $ -$ $ 8)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 8 = 3d - 60$ Solving for $d$ , we get: $2 d = 52$ $d = 26$.